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BITSAT Mathematics Syllabus
The Mathematics syllabus for BITSAT in full: 12 chapters, 45 topics and 58 sub-topics, every one listed below, plus 52 Mathematics flashcards with answers.
Mathematics syllabus: all 12 chapters
Expand any chapter to see its topics and sub-topics.
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Algebra
11 topics- Complex numbers
- Addition
- Multiplication
- Conjugation
- Polar representation
- Properties of modulus and principal argument
- Triangle inequality
- Roots of complex numbers
- Geometric interpretations
- Theory of Quadratic equations
- Quadratic equations in real and complex number system and their solutions
- Arithmetic and geometric progressions
- Arithmetic, geometric and arithmetico geometric series
- Sums of finite arithmetic and geometric progressions
- Infinite geometric series
- Sums of squares and cubes of the first n natural numbers
- Logarithms and their properties
- Exponential series
- Permutations and combinations
- Permutations as an arrangement and combination as selection
- Simple applications
- Binomial theorem for a positive integral index
- Properties of binomial coefficients
- Pascal’s triangle
- Matrices and determinants of order two or three
- Properties and evaluation of determinants
- Addition and multiplication of matrices
- Adjoint and inverse of matrices
- Solutions of simultaneous linear equations in two or three variables
- Elementary row and column operations of matrices
- Types of matrices
- Applications of determinants in finding the area of triangles
- Sets, Relations and Functions
- Algebra of sets applications
- Equivalence relations
- Mappings
- One to one, into and onto mappings
- Composition of mappings
- Binary operation
- Inverse of function
- Functions of real variables like polynomial, modulus, signum and greatest integer
- Mathematical reasoning and methods of proofs
- Mathematically acceptable statements
- Connecting words/phrases – consolidating the understanding of “if and only if (necessary and sufficient) condition”, “implies”, “and/or”, “implied” by”, “and”, “or”, “there exists” and through variety of examples related to real life and Mathematics
- Validating the statements involving the connecting words – difference between contradiction, converse and contra positive
- Mathematical induction
- Linear Inequalities
- Solution of linear inequalities in one variable (Algebraic) and two variables (Graphical)
- Complex numbers
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Trigonometry
3 topics- Measurement of angles in radians and degrees, positive and negative angles, trigonometric ratios, functions with their graphs and identities
- Solution of trigonometric equations
- Inverse trigonometric functions
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Two-dimensional Coordinate Geometry
4 topics- Cartesian coordinates, distance between two points, section formulae, shift of origin
- Straight lines and pair of straight lines
- Equation of straight lines in various forms
- Angle between two lines
- Distance of a point from a line
- Lines through the point of intersection of two given lines
- Equation of the bisector of the angle between two lines
- Concurrent lines
- Circles
- Equation of circle in standard form
- Parametric equations of a circle
- Conic sections
- Parabola, ellipse and hyperbola their eccentricity
- Directrices & foci
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Three dimensional Coordinate Geometry
3 topics- Co-ordinate axes and co-ordinate planes, distance between two points, section formula, direction cosines and direction ratios, equation of a straight line in space and skew lines
- Angle between two lines whose direction ratios are given, shortest distance between two lines
- Equation of a plane, distance of a point from a plane, condition for coplanarity of three lines, angles between two planes, angle between a line and a plane
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Differential calculus
5 topics- Domain and range of a real valued function, Limits and Continuity of the sum, difference and product of two functions, Differentiability
- Derivative of different types of functions
- Polynomial
- Rational
- Trigonometric
- Inverse trigonometric
- Exponential
- Logarithmic
- Implicit functions
- Geometric interpretation of derivative, Tangents and Normal
- Increasing and decreasing functions, Maxima and minima of a function
- Rolle’s Theorem, Mean Value Theorem and Intermediate Value Theorem
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Integral calculus
4 topics- Integration as the inverse process of differentiation, indefinite integrals of standard functions
- Methods of integration
- Integration by substitution
- Integration by parts
- Integration by partial fractions
- Integration by trigonometric identities
- Definite integrals and their properties, Fundamental Theorem of Integral Calculus, applications in finding areas under simple curves
- Application of definite integrals to the determination of areas of regions bounded by simple curves
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Ordinary Differential Equations
3 topics- Order and degree of a differential equation, formulation of a differential equation whole general solution is given, variables separable method
- Solution of homogeneous differential equations of first order and first degree
- Linear first order differential equations
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Probability
4 topics- Various terminology in probability, axiomatic and other approaches of probability, addition and multiplication rules of probability
- Conditional probability, total probability and Baye’s theorem
- Independent events
- Discrete random variables and distributions with mean and variance
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Vectors
3 topics- Direction ratio/cosines of vectors, addition of vectors, scalar multiplication, position vector of a point dividing a line segment in a given ratio
- Dot and cross products of two vectors, projection of a vector on a line
- Scalar triple products and their geometrical interpretations
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Statistics
2 topics- Measures of dispersion
- Analysis of frequency distributions with equal means but different variances
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Linear Programming
2 topics- Various terminology and formulation of linear Programming
- Solution of linear Programming using graphical method, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions
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Mathematical modeling
1 topic- Formulation of simple real life problem, solution using matrices, calculus and linear programming
BITSAT Mathematics flashcards — 52 questions with answers
What is the value of i raised to the powers i^1, i^2, i^3, and i^4?
i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1 (and the pattern repeats with period 4).
For a complex number z = a + bi, what is its modulus |z| and how is the conjugate defined?
Modulus |z| = sqrt(a^2 + b^2); conjugate z-bar = a - bi. Also z·z-bar = |z|^2.
State De Moivre's Theorem for a complex number in polar form.
For z = r(cos θ + i sin θ), z^n = r^n(cos nθ + i sin nθ) for any integer n.
What are the n nth roots of unity and what is their sum?
The nth roots of unity are e^(2πik/n) = cos(2πk/n) + i sin(2πk/n) for k = 0,1,...,n-1. Their sum is 0 (for n ≥ 2).
For the quadratic ax^2 + bx + c = 0, give the formulas for the sum and product of the roots.
Sum of roots = -b/a; product of roots = c/a.
How does the discriminant D = b^2 - 4ac determine the nature of roots of a real quadratic?
D > 0: two distinct real roots; D = 0: two equal real roots; D < 0: two complex conjugate roots.
For a polynomial of degree n with roots, what does Vieta's give for the sum of roots and product of all roots?
Sum of roots = -a_(n-1)/a_n; product of all roots = (-1)^n · a_0/a_n, where a_n is the leading coefficient.
What is the nth term and the sum of n terms of an arithmetic progression (AP)?
nth term a_n = a + (n-1)d; sum S_n = n/2 [2a + (n-1)d] = n/2 (first + last).
What is the nth term and sum of n terms of a geometric progression (GP)?
nth term a_n = a·r^(n-1); sum S_n = a(r^n - 1)/(r - 1) for r ≠ 1.
What is the sum to infinity of a GP and when does it exist?
S_∞ = a/(1 - r), valid only when |r| < 1.
State the AM-GM inequality for two positive numbers a and b.
(a + b)/2 ≥ sqrt(ab), with equality if and only if a = b. (Arithmetic mean ≥ geometric mean.)
Give the formulas for the sum of the first n natural numbers, their squares, and their cubes.
Σn = n(n+1)/2; Σn^2 = n(n+1)(2n+1)/6; Σn^3 = [n(n+1)/2]^2.
What are the formulas for nPr (permutations) and nCr (combinations)?
nPr = n!/(n-r)!; nCr = n!/[r!(n-r)!]. Also nPr = nCr · r!.
State the Binomial Theorem for (a + b)^n where n is a positive integer.
(a + b)^n = Σ_(r=0)^(n) nCr · a^(n-r) · b^r. The general (r+1)th term is T_(r+1) = nCr · a^(n-r) · b^r.
State two key identities for binomial coefficients: the sum of all coefficients and Pascal's rule.
Sum: Σ nCr = 2^n. Pascal's rule: nCr + nC(r-1) = (n+1)Cr.
What conditions make a square matrix invertible, and what is the formula for A inverse?
A is invertible iff det(A) ≠ 0 (non-singular). Then A^(-1) = adj(A)/det(A).
What are symmetric, skew-symmetric, and orthogonal matrices?
Symmetric: A^T = A; skew-symmetric: A^T = -A (diagonal entries are 0); orthogonal: A^T·A = I (so A^(-1) = A^T).
State the key properties of determinants regarding row operations and scalar multiples.
Swapping two rows changes the sign; multiplying a row by k multiplies det by k; det(AB) = det(A)·det(B); det(kA) = k^n·det(A) for n×n matrix.
State Cramer's Rule for solving a system of linear equations.
For AX = B with det(A) = D ≠ 0, each variable x_i = D_i/D, where D_i is D with the i-th column replaced by B.
State De Morgan's laws for sets.
(A ∪ B)' = A' ∩ B' and (A ∩ B)' = A' ∪ B'.
Show the other 32 Mathematics flashcards
How many subsets does a set with n elements have, and how many proper subsets?
Total subsets = 2^n; proper subsets = 2^n - 1 (excluding the set itself).
What is the truth value of a conditional statement p → q (implication)?
p → q is false only when p is true and q is false; otherwise it is true. Its contrapositive (~q → ~p) is logically equivalent.
State the inclusion-exclusion principle for the cardinality of A ∪ B.
n(A ∪ B) = n(A) + n(B) - n(A ∩ B).
State the three fundamental Pythagorean trigonometric identities.
sin^2 θ + cos^2 θ = 1; 1 + tan^2 θ = sec^2 θ; 1 + cot^2 θ = csc^2 θ.
Give the sine and cosine addition formulas: sin(A+B) and cos(A+B).
sin(A+B) = sin A cos B + cos A sin B; cos(A+B) = cos A cos B - sin A sin B.
State the double-angle formulas for sin 2θ and cos 2θ.
sin 2θ = 2 sin θ cos θ; cos 2θ = cos^2 θ - sin^2 θ = 1 - 2sin^2 θ = 2cos^2 θ - 1.
Give the general solution of the trigonometric equation sin θ = sin α.
θ = nπ + (-1)^n α, where n is any integer.
Give the general solutions for cos θ = cos α and tan θ = tan α.
cos θ = cos α ⇒ θ = 2nπ ± α; tan θ = tan α ⇒ θ = nπ + α, where n is any integer.
What are the principal value ranges of sin^(-1)x, cos^(-1)x, and tan^(-1)x?
sin^(-1)x ∈ [-π/2, π/2]; cos^(-1)x ∈ [0, π]; tan^(-1)x ∈ (-π/2, π/2).
State the identity relating sin^(-1)x and cos^(-1)x, and tan^(-1)x and cot^(-1)x.
sin^(-1)x + cos^(-1)x = π/2; tan^(-1)x + cot^(-1)x = π/2 (for x in valid domains).
State the Law of Sines and the Law of Cosines for a triangle.
Law of Sines: a/sin A = b/sin B = c/sin C = 2R. Law of Cosines: c^2 = a^2 + b^2 - 2ab cos C.
Give two formulas for the area of a triangle in terms of its sides/angles.
Area = (1/2)ab sin C; and Heron's formula: Area = sqrt[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2.
What is the slope-intercept form and the point-slope form of a straight line?
Slope-intercept: y = mx + c; point-slope: y - y_1 = m(x - x_1).
What are the conditions for two lines to be parallel and perpendicular in terms of slopes?
Parallel: m_1 = m_2; perpendicular: m_1·m_2 = -1.
What is the perpendicular distance from point (x_1, y_1) to the line ax + by + c = 0?
d = |a·x_1 + b·y_1 + c| / sqrt(a^2 + b^2).
State the standard equation of a circle with centre (h, k) and radius r, and the general form.
Standard: (x-h)^2 + (y-k)^2 = r^2. General: x^2 + y^2 + 2gx + 2fy + c = 0, with centre (-g, -f) and radius sqrt(g^2 + f^2 - c).
Compare the eccentricities of the conic sections (circle, parabola, ellipse, hyperbola).
Circle: e = 0; Parabola: e = 1; Ellipse: 0 < e < 1; Hyperbola: e > 1.
For the parabola y^2 = 4ax, give the vertex, focus, directrix, and length of latus rectum.
Vertex (0,0); focus (a,0); directrix x = -a; length of latus rectum = 4a.
For the ellipse x^2/a^2 + y^2/b^2 = 1 (a > b), give the eccentricity and foci.
e = sqrt(1 - b^2/a^2); foci at (±ae, 0). Sum of focal distances = 2a.
What is the distance formula and the section formula in three-dimensional geometry?
Distance = sqrt[(x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2]. Internal division in ratio m:n: ((mx2+nx1)/(m+n), (my2+ny1)/(m+n), (mz2+nz1)/(m+n)).
What are direction cosines, and what relation do they satisfy?
Direction cosines (l, m, n) are the cosines of the angles a line makes with the x, y, z axes, satisfying l^2 + m^2 + n^2 = 1.
Define the limit condition for continuity of a function f at x = a.
f is continuous at a if lim(x→a) f(x) exists, f(a) is defined, and lim(x→a) f(x) = f(a).
State the two standard trigonometric limits as x → 0.
lim(x→0) (sin x)/x = 1; lim(x→0) (1 - cos x)/x^2 = 1/2.
State the product rule and quotient rule for differentiation.
Product: (uv)' = u'v + uv'. Quotient: (u/v)' = (u'v - uv')/v^2.
State the chain rule for differentiating a composite function y = f(g(x)).
dy/dx = f'(g(x))·g'(x), i.e., dy/dx = (dy/du)·(du/dx).
How do you use the first and second derivatives to find and classify a local extremum?
At a critical point f'(x) = 0: if f''(x) > 0 it's a local minimum; if f''(x) < 0 it's a local maximum; if f''(x) = 0 the test is inconclusive.
State the formula for integration by parts.
∫ u dv = uv - ∫ v du. (Choose u by ILATE order: Inverse, Log, Algebraic, Trig, Exponential.)
State the Fundamental Theorem of Calculus for definite integrals.
If F is an antiderivative of f, then ∫_a^b f(x) dx = F(b) - F(a).
How do you solve a first-order linear differential equation dy/dx + Py = Q?
Use integrating factor IF = e^(∫P dx); solution: y·(IF) = ∫ Q·(IF) dx + C.
Give the formulas for the dot product and cross product of two vectors in terms of the angle θ.
a·b = |a||b| cos θ (scalar); |a×b| = |a||b| sin θ, with a×b perpendicular to both (vector).
State Bayes' theorem and the formula for conditional probability.
Conditional: P(A|B) = P(A∩B)/P(B). Bayes: P(A|B) = P(B|A)·P(A) / P(B).
State the binomial probability distribution: probability of r successes in n trials.
P(X = r) = nCr · p^r · q^(n-r), where q = 1 - p; mean = np, variance = npq.
BITSAT Mathematics FAQ
What is in the BITSAT Mathematics syllabus?
BITSAT Mathematics is split into 12 chapters: Algebra, Trigonometry, Two-dimensional Coordinate Geometry, Three dimensional Coordinate Geometry, Differential calculus, Integral calculus, Ordinary Differential Equations, Probability, Vectors, Statistics, Linear Programming and Mathematical modeling. Together they contain 45 topics and 58 sub-topics.
How many chapters are in BITSAT Mathematics?
12 chapters, containing 45 topics and 58 sub-topics. The largest chapter is Algebra, with 11 topics.
Are there flashcards for BITSAT Mathematics?
Yes — a 52-card Mathematics deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.